There are many different possible approaches to recovering critical data from a failed hard drive or a raid array. Similarly there are a huge number of companies which offer data recovery services advertising both online and also on the high Street, the latter usually offer data recovery as part of a wider range of services including computer repairs, virus removal is etc.
The prices quoted for data recovery give you a good idea of the procedures that will be utilised. Those companies that are dedicated data recovery firms, that is to say data recovery is all that they do, will in the first instance clone your failed hard drive (or hard drives) before carrying out any further work. They are also capable of overcoming physical faults with the hard drives such as bad sectors failed read/write heads or seized platter motors.
The cheaper companies tend only to scan the hard drive that you give them with recovery software and pass you a bundle of files as a result. Some of these may open some may not. In fairness given what they are charging this is all that they can afford to do. However if your data is critical then you need the help of a specialist data retrieval company.